What is the difference between a reflection over a horizontal line and a vertical line?

Let's say that a line of reflection is a vertical line, then a point and its reflection have the same coordinate and If a line of reflection is a horizontal line, then a point and its reflection have the same x-coordinate.

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1